"The double integral can be expressed as in polar coordinates. What is the region R? What is the formula for f(x,y)? What is the integral in cartesian coordinates?
the radius goes from 1 to 2, the angle theta goes from pi to 2pi. thus the region R is the bottom half of the annulus formed by the circles with common center the origin, and radii 1 and 2 (see the diagram below).
since we see that the integral in polar coordinates is . and we know that
i leave the rest to you
can you continue?